Usually we’d be considering non accellerating reference frames. In such frames, the sun and earth both orbit the center of mass of this 2 body system (ignoring the other planets for simplicity).
This center of mass of the sun+earth system lies very near to the center of mass of the sun, because the sun is much more massive than the earth. So saying that the earth orbits the sun is much closer to the truth than the other way around.
However there are cases where it is convenient to use a rotating reference frame. Rotating reference frames have extra forces (pseudo-forces), the centrifugal force and the Coriolis force. The latter explains cyclone weather patterns on earth (The big cloud spirals you see on satellite photo’s).
In an Earth-centric frame of reference, the Sun revolves around Earth. But if you consider the trajectories of the Solar system’s objects, it makes a lot more sense to consider that the central and most massive object should be the origin of your frame of reference. Makes all orbitals almost elliptical in shape, rather than weird insane corkscrew slinkies. But “the Sun revolves around the Earth” is not wrong. It’s just less practical as soon as you consider at least one other planet.
But there is no such thing! At least if you choose your frame of reference ‘correctly’. 
Lovely how a simple discussion can be made complicated when everyone tries hard! 
It’s truly wonderful how we can rise to such pedantry
Hm I believe my knowledge about physics is insufficient to comprehend this. I don’t know about accelerated reference frames, I thought allowing these would lead to some strange implications.
Edit: For example, consider a rotated reference system. Suddenly objects far away from the rotational axis traverse at speed exceeding the speed of light 
In general relativity you sort of ‘replace’ gravity with curvature of space-time. That way, at least locally, there is no more gravity and everything moves on straight lines in the 4 dimensional space time.
Basically:
newtonian physics: space and time are simple, movements can be horribly complex
general relativity: movements are simple (at least locally), space and time become so complex that 99.999% of people claiming to really understand them lie. I totally understand them of course!
So, where did the gravitons go?
I found a remarkable answer to this question, but there is not enough space in the margin of this thread to write it.
I think many celestial bodies revolve, most rotate and almost all spin…
Well, if you take ourselves as a point of reference then it is the earth that revolves around us and not vice-versa. That, of course, would make calculating the movements of all other objects quite the task.
To be fair, the exact fact of the matter is that the Earth and the Sun are spinning around each other, but since the Sun is so much more massive than the Earth, the center of gravity of that system is so close to the Sun that it is practically like we are spinning around it.
The same is true about us and the earth, the earth and the moon and everything else, excluding the gas giants in our solar systems. Actually, recently, this came up :
So, it seems that in reality there is relative a point in space within our solar system, in which nothing usually exists, which everything - including the Sun - spins around, and I find that quite cool
What an insightful video! Appreciated c:
By the way, maybe it should be combined with this one, for some perspective :
We are so used to the illustrated models we had in school, that the actual thing and its scope - both in size and distance - is sometimes mindboggling. 
You’re gonna like this solar system model - sizes and distance to scale, then:
Not in mine 
and Sonne is a lady.
Just
re-
member that you’re standing on a planet that’s evolving
And revolving at 900 miles an hour.
It’s orbiting at 19 miles a second, so it’s reckoned,
The sun that is the source of all our power.
Now the sun, and you and me, and all the stars that we can see,
Are moving at a million miles a day,
In the outer spiral arm, at 40, 000 miles an hour,
Of a galaxy we call the Milky Way.
Okay people, l dont know much about astronomy, but l remembered at the moment that i read that information somewhere, that is why l made this meme. Space is huge, and there are many things that we dont know, and im glad that i opened this discusion with so many great and smart people! Every day you find out something u didnt know before. Have fun everyone!!
I think this is nice too:
